Graphene has attracted widespread attention for supercapacitor applications thank to their excellent conductivity, mechanical flexibility, chemical stability and extremely high specific surface area. Here, all-graphene-oxide-supercapacitors were developed from two reduced graphene oxide (rGO) films as electrodes and one graphene oxide (GO) film as separator. The supercapacitors were then treated with 4M sulfuric acid at temperatures around 80 °C. By this treatment, the sulfuric acid molecules were physically intercalated into both rGO and GO films, which were confirmed by significant decrease intensity of characteristic peaks of sulfuric acid in Raman spectra. These sulfuric-acid-intercalated GO films can function as both quasi-solid-state electrolytes and separators. The average capacitance values measured at 100 mV s−1 of the thermally wetted supercapacitor at 84 °C is improved 93.7 times higher than that of the as-prepared all-graphene-oxide-supercapacitor. The maximum capacitance of 266 F cm−3 is obtained at scan rate 10 mV s−1 for the thermally wetted supercapacitor at 84 °C. To the best of our knowledge, this is the highest specific capacitance that has ever been reported for a graphene oxide-based supercapacitor. Importantly, being in a quasi-solid-state, the energy storage performance of supercapacitors are persistent over several thousand cycles, making it very much unlike other carbon-based supercapacitors.